Simplify the following expression: $y = \dfrac{-2k^2 + 22k - 36}{k - 9} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-2$ , so we can rewrite the expression: $ y =\dfrac{-2(k^2 - 11k + 18)}{k - 9} $ Then we factor the remaining polynomial: $k^2 {-11}k + {18} $ ${-9} {-2} = {-11}$ ${-9} \times {-2} = {18}$ $ (k {-9}) (k {-2}) $ This gives us a factored expression: $\dfrac{-2(k {-9}) (k {-2})}{k - 9}$ We can divide the numerator and denominator by $(k + 9)$ on condition that $k \neq 9$ Therefore $y = -2(k - 2); k \neq 9$